非负矩阵分解及在人脸识别的应用PPT格式课件下载.ppt

1、D.D.Lee andS.Seung,”Learning the parts of objects by non-negative matrix factorization”Nature,vol.401,pp.788-791,1999作者的相关信息Daniel D.Lee,Ph.D.lAssociate ProfessorDept.of Electrical and Systems EngineeringDept.of Bioengineering（Secondary）GRASP（General Robotics,Automation,Sensing,Perception）Labl203B M

2、oore/6314University of Pennsylvania200 S.33rd StreetPhiladelphia,PA 19104215-898-8112215-573-2068（FAX）lEmail:ddleeseas.upenn.edu lhttp:/www.seas.upenn.edu/ddlee/H.Sebastian Seung lProfessor of Computational Neuroscience,MITInvestigator,Howard Hughes Medical InstitutelMIT,46-506543 Vassar St.Cambridg

3、e,MA 02139voice:617-252-1693seungmit.edulAdministrative assistant:Amy Dunnvoice:617-452-2694fax:617-452-2913adunnmit.edulhttp:/hebb.mit.edu/people/seung/Problem StatementGiven a set of images:1.Create a set of basis images that can be linearly combined to create new images2.Find the set of weights t

4、o reproduce every input image from the basis images3.Dimension reduction lPCAlNMFlLNMFlFNMFlWNMFMainly DiscussPCAlFind a set of orthogonal basis imageslThe reconstructed image is a linear combination of the basis images What dont we like about PCA?lPCA involves adding up some basis images then subtr

5、acting otherslBasis images arent physically intuitivelSubtracting doesnt make sense in context of some applicationslHow do you subtract a face?lWhat does subtraction mean in the context of document classification?backNon-negative Matrix FactorizationlLike PCA,except the coefficients in the linear co

6、mbination cannot be negativeNon-negative matrix factorization（NMF）（Lee&Seung-2001）NMF gives Part based representation（Lee&Seung Nature 1999）NMF is based on Gradient DescentNMF:VWH s.t.Wi,d,Hd,j0Let C be a given cost function,then update the parameters according to:The idea behind multiplicative upda

7、tesPositive termNegative termThe NMF decomposition is not uniqueNMF only unique when data adequately spans the positive orthant（Donoho&Stodden-2004）NMF Basis Imagesnmf_basislOnly allowing adding of basis images makes intuitive senseHas physical analogue in neuronslForcing the reconstruction coeffici

8、ents to be positive leads to nice basis imagesTo reconstruct images,all you can do is add in more basis imagesThis leads to basis images that represent partsFaceslTraining set:2429 exampleslFirst 25 examples shown at rightlSet consists of 19x19 centered face imagesFaceslBasis Images:Rank:49Iteration

9、s:50Facesx=OriginalFacesx=OriginalbackbackExampleLocal non-negative matrix factorizationLettingLNMF is aimed at learning local features by imposing the following three additional constraints on the NMF basis:backbackLNMF_basisLNMF_basisFisher non-negative matrix factorizationbackbackWeighted NMFback

10、back结论及未来工作l综上所述，非负矩阵分解是一种的提取图像局部特征信息的有效的方法，目前在很多领域得到广泛应用，值得我们关注。l问题（1）非平衡样本集识别率低的问题（2）权重选取问题参考文献l1D.D.Lee and H.S.Seung,“Learning the parts of objects by non-negative matrix factorization”,Nature,vol.401,pp.788-791,1999l2D.D.Lee and H.S.Seung“Algorithms for non-negativeMatrix factorization”，in Proc

11、eedings of Neural Information Processing Systems,2000.l3S.Z.Li,X.Hou,H.J.Zhang,andQ.Cheng,“Learning spatially localized,parts-based representation”,Proc.IEEE Int.Conf.ComputerVision and Pattern Recognition,2001,pp.207-212l4J.Lu andY.-P.Tan,“Doubly weighted nonnegative matrix factorization for imbalanced face recognition”,Proc.IEEE Int.Conf.Acoustics,Speech,andSignalProcessing,2009,pp.877C880